Consider the single-factor production function, Y = AL, for islands A and B. Each island has 100 units of labor (and they cannot move across islands). Island A can produce one unit of agricultural product with 4 units of labor and can produce one unit of electronic product with 2 units of labor (i.e., A is 1/4 for agriculture and 1/2 for electronics). Island B can produce one unit of agricultural product with 5 units of labor and produce one unit of electronic product with 4 units of labor (i.e., A is 1/5 for agriculture and 1/4 for electronics). People on both islands must consume both goods, for example, if no agricultural product is produced, its price will go to infinity. Assume the two islands can trade with each other at no cost. Please note that Island A and A (in italics) are different, with the latter representing (in this production function) the amount of labor effort required to make one or the other goods.

(a) What are A's and B's respective comparative advantages?

(b) Please calculate the range of the possible relative prices (pa/pe) for the two kinds of goods.

(C) Letting Pa/pe = 1.5, show how many units of each product people will produce on each island

(d) Using the relative price above, calculate the relative wage for Islands A and B, wa/WB.

(e) Each unit of labor needs to consume unvaryingly 0.1 unit of agricultural production, and as many electronic products as possible. Use the relative price above, calculate and compare the electronic product people on each island can consume with and without trade.

(f) Island A is more productive (uses less labor) in the production of both goods compared to Island B. In one sentence, why would A and B trade with each other under these circumstances?